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MattWillFlood committed Jan 8, 2024
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101 changes: 19 additions & 82 deletions docs/_build/html/python/Functions/Bidimensional.html
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@@ -464,107 +464,49 @@ <h2>Functions for estimating the entropy of a two-dimensional univariate matrix.
</dd>
<dt class="field-odd">Fx<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p>Fuzzy function name, one of the following strings:</p></li>
<li><p>Fuzzy funtion name, one of the following:</p></li>
</ul>
<p>{<code class="docutils literal notranslate"><span class="pre">'sigmoid'</span></code>, <code class="docutils literal notranslate"><span class="pre">'modsampen'</span></code>, <code class="docutils literal notranslate"><span class="pre">'default'</span></code>, <code class="docutils literal notranslate"><span class="pre">'gudermannian'</span></code>, <code class="docutils literal notranslate"><span class="pre">'bell'</span></code>, <code class="docutils literal notranslate"><span class="pre">'triangular'</span></code>, <code class="docutils literal notranslate"><span class="pre">'trapezoidal1'</span></code>, <code class="docutils literal notranslate"><span class="pre">'trapezoidal2'</span></code>, <code class="docutils literal notranslate"><span class="pre">'z_shaped'</span></code>, <code class="docutils literal notranslate"><span class="pre">'gaussian'</span></code>, <code class="docutils literal notranslate"><span class="pre">'constgaussian'</span></code>}</p>
<p>{<code class="docutils literal notranslate"><span class="pre">'sigmoid'</span></code>, <code class="docutils literal notranslate"><span class="pre">'modsampen'</span></code>, <code class="docutils literal notranslate"><span class="pre">'default'</span></code>, <code class="docutils literal notranslate"><span class="pre">'gudermannian'</span></code>, <code class="docutils literal notranslate"><span class="pre">'linear'</span></code>}</p>
</dd>
<dt class="field-even">r<span class="colon">:</span></dt>
<dd class="field-even"><ul class="simple">
<li><p>Fuzzy function parameters, a 1 element scalar or a 2 element vector of positive values.</p></li>
</ul>
<dl class="simple">
<dt>The <code class="docutils literal notranslate"><span class="pre">r</span></code> parameters for each fuzzy function are defined as follows: [default: (.2 2)]</dt><dd><ul class="simple">
<li><dl class="simple">
<dt>default: [Tuple]</dt><dd><ul>
<li><p>r(1) = divisor of the exponential argument</p></li>
<li><p>r(2) = argument exponent (pre-division)</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>sigmoid: [Tuple]</dt><dd><ul>
<li><p>r(1) = divisor of the exponential argument</p></li>
<li><p>r(2) = value subtracted from argument (pre-division)</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>modsampen: [Tuple]</dt><dd><ul>
<li><p>r(1) = divisor of the exponential argument</p></li>
<li><p>r(2) = value subtracted from argument (pre-division)</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>gudermannian: </dt><dd><ul>
<li><p>r = a scalar whose value is the numerator of argument to gudermannian function: GD(x) = atan(tanh(r/x)). GD(x) is normalised to have a maximum value of 1.</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>triangular: </dt><dd><ul>
<li><p>r = a scalar whose value is the threshold (corner point) of the triangular function.</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>trapezoidal1: </dt><dd><ul>
<li><p>r = a scalar whose value corresponds to the upper (2r) and lower (r) corner points of the trapezoid.</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>trapezoidal2: [Tuple]</dt><dd><ul>
<li><p>r(1) = a value corresponding to the upper corner point of the trapezoid.</p></li>
<li><p>r(2) = a value corresponding to the lower corner point of the trapezoid.</p></li>
</ul>
</dd>
</dl>
</li>
<p>The <code class="docutils literal notranslate"><span class="pre">r</span></code> parameters for each fuzzy function are defined as follows:</p>
<blockquote>
<div><ul class="simple">
<li><dl class="simple">
<dt>z_shaped: </dt><dd><ul>
<li><p>r = a scalar whose value corresponds to the upper (2r) and lower (r) corner points of the z-shape.</p></li>
</ul>
<dt>sigmoid: </dt><dd><p>r(1) = divisor of the exponential argument
r(2) = value subtracted from argument (pre-division)</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>bell: </dt><dd><ul>
<li><p>r(1) = divisor of the distance value</p></li>
<li><p>r(2) = exponent of generalized bell-shaped function</p></li>
</ul>
<dt>modsampen: </dt><dd><p>r(1) = divisor of the exponential argument
r(2) = value subtracted from argument (pre-division)</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>gaussian: </dt><dd><ul>
<li><p>r = a scalar whose value scales the slope of the Gaussian curve.</p></li>
</ul>
<dt>default: </dt><dd><p>r(1) = divisor of the exponential argument
r(2) = argument exponent (pre-division)</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>constgaussian: </dt><dd><ul>
<li><p>r = a scalar whose value defines the lower threshod and shape of the Gaussian curve.</p></li>
</ul>
<dt>gudermannian: </dt><dd><p>r = a scalar whose value is the numerator of argument to gudermannian function:
GD(x) = atan(tanh(r/x)). GD(x) is normalised to have a maximum value of 1.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>[DEPRICATED] linear: </dt><dd><p>r = an integer value. When r = 0, the argument of the exponential function is
<dt>linear: </dt><dd><p>r = an integer value. When r = 0, the argument of the exponential function is
normalised between [0 1]. When r = 1, the minimuum value of the exponential argument is set to 0.</p>
</dd>
</dl>
</li>
</ul>
</dd>
</dl>
</div></blockquote>
</dd>
<dt class="field-odd">Logx<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
@@ -598,11 +540,6 @@ <h2>Functions for estimating the entropy of a two-dimensional univariate matrix.
41st Annual International Conference of the IEEE (EMBC) Society
2019.</p>
</dd>
<dt>[3] Hamed Azami, et al.</dt><dd><p>“Fuzzy Entropy Metrics for the Analysis of Biomedical Signals:
Assessment and Comparison”
IEEE Access
7 (2019): 104833-104847</p>
</dd>
</dl>
</dd>
</dl>
@@ -662,16 +599,16 @@ <h2>Functions for estimating the entropy of a two-dimensional univariate matrix.
</dl>
</div></blockquote>
<dl>
<dt><strong>NOTE</strong>: </dt><dd><p><code class="docutils literal notranslate"><span class="pre">The</span> <span class="pre">original</span> <span class="pre">bidimensional</span> <span class="pre">permutation</span> <span class="pre">entropy</span> <span class="pre">algorithms</span> <span class="pre">[1][2]</span></code>
<code class="docutils literal notranslate"><span class="pre">do</span> <span class="pre">not</span> <span class="pre">account</span> <span class="pre">for</span> <span class="pre">equal-valued</span> <span class="pre">elements</span> <span class="pre">of</span> <span class="pre">the</span> <span class="pre">embedding</span> <span class="pre">matrices.</span></code>
<dt><strong>NOTE</strong> - <a href="#id1"><span class="problematic" id="id2">``</span></a>The original bidimensional permutation entropy algorithms </dt><dd><p>[1][2] do not account for equal-valued elements of the embedding
matrices. ``
To overcome this, PermEn2D uses the lowest common rank for
such instances. For example, given an embedding matrix A where,
A = [3.4 5.5 7.3]</p>
<blockquote>
<div><p>[2.1 6 9.9]
<div><p><a href="#id3"><span class="problematic" id="id4">|2.1 6 9.9|</span></a>
[7.3 1.1 2.1]</p>
</div></blockquote>
<p>would normally be mapped to an ordinal pattern like so,
<p>would normally be mapped to an ordinal pattern like so,
[3.4 5.5 7.3 2.1 6 9.9 7.3 1.1 2.1] =&gt;
[ 8 4 9 1 2 5 3 7 6 ]
However, indices 4 &amp; 9, and 3 &amp; 7 have the same values, 2.1
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